Estimation of the Structure of Hydrophobic Surfaces Using the Cassie-Baxter Equation

The effect of extreme water repellency, called the lotus effect, is caused by the formation of a Cassie-Baxter state in which only a small portion of the wetting liquid droplet is in contact with the surface. The rest of the bottom of the droplet is in contact with air pockets. Instrumental methods are often used to determine the textural features that cause this effect-scanning electron and atomic force microscopies, profilometry, etc. However, this result provides only an accurate texture model, not the actual information about the part of the surface that is wetted by the liquid. Here, we show a practical method for estimating the surface fraction of texture that has contact with liquid in a Cassie-Baxter wetting state. The method is performed using a set of ethanol-water mixtures to determine the contact angle of the textured and chemically equivalent flat surfaces of AlSI 304 steel, 7500 aluminum, and siloxane elastomer. We showed that the system of Cassie-Baxter equations can be solved graphically by the wetting diagrams introduced in this paper, returning a value for the texture surface fraction in contact with a liquid. We anticipate that the demonstrated method will be useful for a direct evaluation of the ability of textures to repel liquids, particularly superhydrophobic and superoleophobic materials, slippery liquid-infused porous surfaces, etc.